The prime minister told reporters at the NATO summit in Prague Friday that Francoise Ducros has apologized to him for causing an international fuss.
"She said to me she had a private conversation and she was defending in the discussion somewhat the president of the United States," Chretien told reporters. "She doesn't remember having used these words.
"She said to me that if it's causing too much of a problem, she offered her resignation, and I did not accept that because it was a private conversation."
For her part, Ducros says she did not insult the American president.
"I have never, in any of the many briefings I have given reporters as the prime minister's chief spokesperson, ever expressed, on the record or off the record, any negative opinion concerning President George Bush," she wrote in her letter of resignation.
"If I made comments in the context of what I understood to be a private conversation, I regret that they have attracted so much media attention," she added. "I accept full responsibility for them and I sincerely apologize."
The furore erupted after Ducros reportedly made the comment in an off-the-record media briefing, after President Bush suggested NATO members should spend more on defense.
It may have been uttered in a private conversation with a Canadian reporter, but other journalists in the room heard it and the comment quickly made headlines around the world.
"It simply does not get more serious," said CTV correspondent Craig Oliver, who heard Ducros' remark.
"This woman is the voice of the Canadian government, she has mortally insulted the leader of the free world -- and she has perhaps provided comfort to the enemies of the U.S."
While the Canadian prime minister tried to play down the incident, opposition critics were aghast at his refusal to accept Ducros' resignation.
"The problem is a string of anti-Americanism coming from people in senior positions with the Liberal government," said Canadian Alliance MP Jason Kenney. "These sort of comments just further impair a relation we need to build."
Tory leader Joe Clark said Ducros should have been promptly put on a plane back to Canada and fired.
"Trained diplomats lose their positions. Elected members of Parliament lose their positions, (but) Francie Ducros keeps hers? Where's the logic in that?" Clark asked.
"Jean Chretien is keeping her there because of a double standard that is undermining the government."
Chretien, Ducros and the Canadian entourage are expected to return to Ottawa from Prague over the weekend.